3. You measure the weights of 24 male runners. You do not actually choose an SRS

Question

3. You measure the weights of 24 male runners. You do not actually choose an SRS, but you are willing to assume that these runners are a random sample from the population of male runners in your town or city. Here are their weights in kilograms: 67.8 61.9 63.0 53.1 62.3 59.7 55.4 58.9 60.9 69.2 63.7 68.3 64.7 65.6 56.0 57.8 66.0 62.9 53.6 65.0 55.8 60.4 69.3 61.7 a) Suppose that the standard deviation of the population is known to be sigma = 4.5 kg. what is sx, the standard error of x? b) Give a 95% confidence interval for the mean of the population from which the sample is drawn. c) Are you quite sure that the average weight of the population of runners is less than 65 kgi? 67.8 61.9 63.0 53.1 62.3 592.7 55.4 58.9

Explanation / Answer

3.

a)

SE(x) = sigma/sqrt(n) = 4.5/sqrt(24) = 0.918558654 [ANSWER]

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b)

Note that              
              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    61.79166667          
t(alpha/2) = critical t for the confidence interval =    2.499866739          
s = sample standard deviation =    4.5          
n = sample size =    24          
df = n - 1 =    23          
Thus,              
              
Lower bound =    59.49539244          
Upper bound =    64.08794089          
              
Thus, the confidence interval is              
              
(   59.49539244   ,   64.08794089   ) [ANSWER]

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c)

YES, BECAUSE THE WHOLE INTERVAL IS LESS THAN 65.

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